A few straightforward, little estimated robot are less demanding, less expensive to manufactured, than a solitary substantial effective robot framework; Overall framework can be more vigorous and dependable. ...

Motivation • Examples of Multi-robot groups: • Tasks are too complex; • Gain in overall performance; • Several simple, small-sized robot are easier, cheaper to built, than a single large powerful robot system; • Overall system can be more robust and reliable. • Group Cooperation in Nature: Armies of Ants Schools of Fish Flocks of Birds • How do we incorporate similar cooperation in artificial multi robot group? Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Motion Planning (MP) for Robot Collectives • Definition: • The process of selecting a motion and the associated set of input forces and torques from the set of all possible motions and inputs while ensuring that all constraints are satisfied. • Why Motion Planning? • To realize all the functionalities for mobile robots, the fundamental problem is getting a robot to move from one location to another without colliding with obstacles. • MP for Robot Collective - • MP exist for individual robots such as manipulator, wheeled mobile robot (WMR), car-like robot, etc. • We want to examine extension of MP techniques to • Robot Collectives Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

Research Issues • Broad Challenges: • Extending APF approach for Multi-robot collectives. • Ensuring tight formations required for Cooperative Payload Transport application. • Specific Research Questions: • Which type of potential function is more suitable for MP for multi robot groups? • How can we use the APF framework to help maintain formation? and • How this framework be extended to realize the tight formation requirement for cooperative payload transport? Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

Research Issues (cont’) • To answer these research questions: • Part I: • Study various APF & their limitations; • Determined a suitable APF as our test bed; • Create a GUI to design and visualize the potential field; • Case studies: MP for single robot using APF approach. • Part II: • E.O.M. for group of robots with formation constraints; • Solved the MP planning problem using three approaches; • Performance evaluation using various case studies. Introduction Model Distribution Analysis Manipulability Cooperative System Conclusion

Local APF Approach-Formulation • Idea: • Goal generate an attractive potential well; • Obstacle generate repulsive potential hill; • Superimpose these two type of potentials give us the total potential of the workspace. Where: denote the total artificial potential field; denote the attractive potential field; and is the repulsive potential field. is the position of the robot. Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Local APF -Attractive potential • Characteristics: • Affect every point on the configuration space; • Minimum at the goal. • The gradient must be continuous. Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Local APF -Attractive potential • Example 1: Where: = Positive scaling factor = Euclidean distance between the robot and the target = Position of the target. = Position of the robot. is commonly used. Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Local APF -Repulsive potential • Characteristics: • The potential should have spherical symmetry for large distance; • The potential contours near the surface should follow the surface contour; • The potential of an obstacle should have a limited range of influence; • The potential and the gradient of the potential must be continuous. Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Local APF -Repulsive potential • Example 4 - Ge New Function: Where: = Minimal Euclidean distance from robot to the target. • Modified from FIRAS function to solve the ‘Goal NonReachable for Obstacle Nearby’ -GNRON problem. • Ensures that the total potential will reach its global minimum, if and only if the robot reaches the target where Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Local APF –Total Potential • Total Potential of Workspace: • Superimpose different repulsive potential from obstacles and different attractive potential from the goal, we get the total potential for the workspace. • At any point of the workspace, the robot will reach the target byfollowing the negative gradient flow of the total potential. Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Global APF – Navigation Function [ Proposed by: Rimon & Koditschek] • Properties: • Guarantee to provide a global minimum at target. • Bounded maximum potential. Let be a robot free configuration space, and let be a goal point in the interior of , A map is a Navigation Function if it is: . function. , that is, at least a 1. Smooth on . 2. Polar at ,i.e., has a unique minimum at on the path-connected component of containing , i.e., uniformly maximal on the boundary of 3. Admissible on 4. A Morse Function Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Feature: Tunable by a single parameter : Navigation Function • Navigation Function of a sphere world : Where: Detail is the implicit form of bounding sphere. is the implicit form of obstacle geometric Eq. Number of obstacles Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

APF Approach – Formulation & Simulation • Idea: • We want the robot to follow the negative gradient flow of the workspace potential field; • Analogy to a ball rolling down to the lowest point in a given potential. • Thus the gradient information will serve as the input to the robot system. Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

APF Approach – Formulation • Formulation – Single point-mass robot: Kinematic Model: Dynamic Model: is a positive diagonal scaling matrix is the gradient of the potential field is dissipative term added to stabilize the system Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

PART II: Group Robots Dynamic Formulation • Include: • Dynamic Formulation for Group of Robots with Formation; • Solved the E.O.M using three Methods; • Simulation Studies; • Performance evaluation of each Methods.

Group Robots Dynamic Formulation • The dynamic of group of robot can be formulated using Lagrange Equation by: (1) is the n-dimensional vector of generalized coordinates is the n-dimensional vector of generalized velocities is the n-dimensional vector of generalized velocities is the n-dimensional vector of external forces is the vector of input forces, which is is the Jacobian matrix Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion

Group Robots Dynamic Formulation • Method II: Penalty Formulation Approach: • The holonomic constraints are relaxed and replaced by linear/non-linear spring with dampers. • Here, the Lagrange multipliers are explicitly approximated as the force of a virtual spring or damper based on the extent of the constraint violation and assumed spring stiffness and damping constant. This can be expressed as: Resulting Dynamic Equation: (4) Introduction APF Approaches Group Robot Formulation Simulation Results Conclusion